Assessing the effects of pandemic risk on cooperation and social norms using a before-after Covid-19 comparison in two long-term experiments

How does threat from disease shape our cooperative actions and the social norms that guide such behaviour? To study these questions, we draw on a collective-risk social dilemma experiment that we ran before the emergence of the Covid-19 pandemic (Wave 1, 2018) and compare this to its exact replication, sampling from the same population, that we conducted during the first wave of the pandemic (Wave 2, 2020). Tightness-looseness theory predicts and evidence generally supports that both cooperation and accompanying social norms should increase, yet, we mostly did not find this. Contributions, the probability of reaching the threshold (cooperation), and the contents of the social norm (how much people should contribute) remained similar across the waves, although the strength of these social norms were slightly greater in Wave 2. We also study whether the results from Wave 1 that should not be affected by the pandemic—the relationship between social norms and cooperation and specific behavioural types—replicate in Wave 2 and find that these results generally hold. Overall, our work demonstrates that social norms are important drivers of cooperation, yet, communicable diseases, at least in the short term, have little or no effects on either.


Experimental design
Both experiments follow an identical design (Fig. 1).Subjects participate in multiple stages of the experiment across 30 days.During day 1 they complete the Big Five questionnaire 33,34 , an incentivised risk preference elicitation task 35 , the autism spectrum quotient questionnaire 36,37 , the six item slider Social Value Orientation task 38 , and a demographic questionnaire.These measures serve to separate individual motives and preferences from social norm explanations.In the following 28 days (day 2-29), subjects are each endowed with 100 points, randomly allocated into groups of six each day, and are asked to contribute between 0-100 points to prevent a collective loss from occurring with a particular risk.If a total of 300 points were contributed (i.e., an average of 50 points per subject), the disaster was averted with certainty and subjects kept all points that they did not contribute.If the threshold of 300 points was not reached, with some probability subjects lost everything.After each round, subjects receive feedback about the contribution of all the other subjects in their group, whether the threshold has been reached or not, whether the catastrophe occurred or not, and their individual payoffs for that round.They were then randomly re-grouped and began a new round of the experiment.They were not informed about the behaviour of those outside their group.The experiment's instructions are reported in section S1.1 in the Supplementary Materials.
Every day, we also measured subjects' personal normative beliefs ("How much one ought to contribute to prevent the collective loss"), empirical expectations ("How much you think others in your group actually contribute to preventing the collective loss"), and normative expectations ("How much you think others in your group think that one ought to contribute to prevent the collective loss") 32,39 .The latter two expectations are key elements of social norms whilst we measure the former in order to separate one's own beliefs from socially held expectations.The order of norm-elicitation and behavioural experiments may influence the norms and behaviours observed.Eliciting norms post-behaviour may lead to biases like self-serving ones 40 , while doing so pre-behaviour can cause people to overemphasise prevailing norms 41 , affecting their behaviour due to situational cues biases.To mitigate these biases, we randomly varied the order of eliciting people's beliefs relative to their behavioural choices.On selected days (1, 5, 10, 14, 15, 19, 24), we also used the strategy method to elicit subjects' conditional contributions based on different combinations of their group members' behaviour and normative expectations (e.g."How much do you contribute if most of the other people in your group contribute more than 50 and think that you should contribute more than 50").When subjects respond to these questions, they do not know their group members' behaviour nor their normative expectations, but, since we record these, we can implement their choice based on the contribution and expectations of others in their group.That is, this conditional contribution stage is incentivised and subjects know this (see Section S1.2 in the Supplementary Materials for details about the social norm belief elicitation method).On the final day of the experiment, we measure subjects' preferences for punishing by allocating points to reduce the payoffs, at a 1:3 ratio, of a randomly selected other who contributed less than 50, 50, or more than 50.We also measure subjects' expectations of how others behave in the punishment task.These expectations, again, were incentivised.Orientation, and completed a short questionnaire.From day 2 to day 29 participants were matched in groups of six people and interacted according to the collective risk social dilemma answering questions on their expectations (asked in a random order with 50/50 probability either before or after the contribution decision) and deciding their actual contribution and their conditional contributions.Conditional contributions were elicited on rounds 1, 5, 10, 14, 15, 19, 24, and 28.At the end of each round, participants kept their saved points if the threshold was reached, otherwise they lost all their round points with probability p.The outcome of the conditional contribution decisions was calculated based on the contributions and actual empirical and normative expectations of each group (see Supplementary Information Section S1 for details).Each day the groups were reshuffled.On day 30, participants went through a punishment phase in which their punishment behaviour and expectations were elicited.Subjects subsequently received information about their results and payment.Figure reproduced from 18 .
Vol:.(1234567890)The treatments were a mixed within and between-subjects design.Specifically, both the severity (within-subjects) and the order of the risk (between-subjects) were manipulated: in the High Low treatment subjects first face a 90% risk (rounds 1-14) and then a 60% risk (rounds 15-28) while in the Low High treatment this is reversed.
In addition to the causal relationship between increased levels of risk and cooperation, the original study reported in Ref. 18 found that (1) empirical and normative expectations are positively associated with cooperation; (2) changing empirical and normative expectations changed cooperation; (3) punishment was targeted at low contributors and subjects anticipated this; (4) the stronger social norms that emerged under high risk made cooperative behaviour "sticky", leading to a slower change in cooperation after a decrease in risk than the other way around (when risk increased, cooperative behaviour increased immediately); and (5) a specific combination of behavioural types emerged: empirical cooperators (increase cooperation in response to higher empirical expectations), normative cooperators (increase cooperation in response to higher normative expectations), social norm followers (increase cooperation in response to the combination of higher empirical and normative expectations), unconditional types (do not respond to empirical or normative expectations), and thresholddriven types (reduce their cooperation in response to higher empirical expectations).While compelling, these results rest entirely on risk that is experienced through monetary incentives: a higher probability of the collective loss event implies a higher probability of losing one's earnings.Yet it remains unclear whether the same finding holds when the threat stems from a risk, due to the threat of Covid-19, that can physically harm individuals.

Predictions
All hypotheses reported below were pre-registered at the Open Science Framework (https:// osf.io/ pufhm).Our first set of hypotheses concern outcomes that we expected to change between the two waves.Based on existing results that cooperation may increase after disasters, potentially including diseases, we anticipated that: • Contributions will be higher in Wave 2 than in Wave 1 (Hypothesis 1).
• Groups are likelier to reach the threshold (i.e., to cooperate) in Wave 2 than in Wave 1 (Hypothesis 2).
Additionally, based on tightness-looseness theory, we predicted that: • Average empirical expectations will be higher in Wave 2 than in Wave 1 (Hypothesis 3).
• Average normative expectations will be higher in Wave 2 than in Wave 1 (Hypothesis 4).
• The strength of group-level social norms will be higher in Wave 2 than in Wave 1 (Hypothesis 5).
By social norms strength, we mean here a combination of three factors.First, consistency: the extent to which people's beliefs (empirical and normative expectations) within a group are consistent with each other's.Second, accuracy: the degree to which these beliefs accurately capture reality.Empirical expectations should reflect the group's actual contributions and normative expectations should reflect the group's personal normative beliefs.Third, specificity: the variance in the distribution of beliefs.The specific operationalization is taken from 18 (see Supplementary Materials Section S1.3 for details).
We also anticipated that a number of other outcomes should not change between the two waves.In other words, some findings from Wave 1 should replicate in Wave 2. The first part of these expectations concern the behavioural types that were previously identified: empirical cooperators (increase cooperation in response to higher empirical expectations), normative cooperators (increase cooperation in response to higher normative expectations), social norm followers (increase cooperation in response to the combination of higher empirical and normative expectations), unconditional types (do not respond to empirical or normative expectations), and threshold-driven types (reduce their cooperation in response to higher empirical expectations).If we find these types again in Wave 2 then all types (but particularly normative cooperators and social norm followers) increase cooperation in response to higher normative expectations, and so we anticipate that: • Increasing normative expectations generally enhances cooperation (Hypothesis 6a).
Instead, for increasing empirical expectations, empirical cooperators and social norm followers should increase their cooperation while threshold-driven types should reduce their contributions.Thus, we expected that: • Increasing empirical expectations will decrease cooperation for some types of subjects and increase it for others.That is, the effect of empirical expectations on cooperation is more heterogeneous than the effect of normative expectations on cooperation (Hypothesis 6b).
Finally, the relationship between social norms and cooperation should not change either.Specifically, we should replicate that (1) empirical and normative expectation are positively associated with cooperation, (2) changing empirical and normative expectations changes cooperation, (3) punishment is targeted at low contributors and subjects anticipated this, and (4) stronger social norms developed under high risk make cooperative behaviour "sticky", leading to a slower change in cooperation after a decrease in risk than after an increase in risk.

Results
We start by presenting the outcomes that we anticipated to change between the waves: contributions (H1), the probability that groups reach the threshold (H2), empirical expectations (H3), normative expectations (H4), and the strength of norms (H5).We then turn to the factors that we expected to remain comparable across the waves: behavioural types, the causal effect of empirical and normative expectations on contributions (H6a and H6b), and the relationship between social norms and cooperation.Table 1 qualitatively summarises the result for all preregistered hypotheses.Table 2 reports for Hypotheses 1-5 the predicted estimates in Wave 1 (column ŷWave1 ) and in Wave 2 (column ŷWave2 ) and the regression coefficient for the wave difference.For each depend- ent variable, it first reports the overall effect of our preregistered hypotheses (All) and then proceeds with the results of exploratory analyses that compare the wave differences across treatments and risk levels (based on three-way interactions).Finally, Fig. 2 and 3 display the results of Hypotheses 1-5 visually in correlation plots that contrast the per-round correlation between Wave 1 (horizontal axis) and Wave 2 (vertical axis) for each round of the High Low (blue) and Low High treatment (red) for 90% risk (diamonds) and 60% risk (squares).Given this configuration, our hypotheses predict that the points on the figures should consistently lie above the 45 • diagonal line.Detailed analyses including the effects of all control variables for all hypotheses are documented in the Supplementary Materials (Section S2).The Supplementary Materials also report the results of the replication analyses (Section S3) and of additional summary statistics and exploratory analyses (Section S4).
Table 1.Summary of our hypotheses and findings.

Hypotheses Results
Contribution and probability of reaching the threshold H1 Contributions will be higher in Wave 2 Not supported H2 Probability of reaching the threshold will be higher in Wave 2 Not supported

H3
Average empirical expectations will be higher in Wave 2 Not supported H4 Average normative expectations will be higher in Wave 2 Not supported

H5
Strength of group-level social norms will be higher in Wave 2 Supported

H6a
Increasing normative expectations will increase contributions Supported

H6b
Increasing empirical expectations will decrease contributions for some subjects and increase it for others Supported

Contribution and probability of reaching the threshold
We find no increase in contributions between Wave 1 and Wave 2 ( ŷWave1 = 49.59 , ŷWave2 = 50.36; b All = 0.768, p = 0.171 , 95% CI [−0.33, 1.87] ) so do not find support for Hypothesis 1.To explore the lack of average differences, we check whether contributions varied across the waves according to risk level and treatment.We find that the predicted contributions in Wave 1 when the risk was 90% were greater than 50 in both treatments (Low High 90%: ŷWave1 = 50.84, High Low 90%: ŷWave1 = 50.75 ) implying that average contributions were already sufficiently high in Wave 1 under 90% risk to, in expectation, avert the possibility of a collective loss.
Given the threshold at 300, any increase over 50 would result in inefficient cooperation (i.e., because resources are wasted).Consequently, and unsurprisingly, cooperation did not increase further in Wave 2 when risk was 90% (Low High 90%: ŷWave2 = 51.63 , High Low 90%: ŷWave2 = 51.55 ; comparisons to Wave 1 n.s.).Under 60% risk of collective loss, average contributions in Wave 1 were always below 50 (Low High 60%: ŷWave1 = 48.38 , High Low 60%: ŷWave1 = 48.39 ), thus allowing room for improvement.In Wave 2 contributions approached, but did not reach, 50 in Low High 60% of Wave 2 ( ŷWave2 = 49.87 , comparison to Wave 1 n.s.), and failed to reach 50 in High Low 60% of Wave 2 ( ŷWave2 = 48.37 , comparison to Wave 1 n.s.).Thus, the increase in contribution that we anticipated to see did not materialise: neither on average nor in the specific risk and treatment combinations.
Result 1: Contributions were not higher in Wave 2 than in Wave 1, neither on average nor broken down by treatment and risk level.Table 2. Summary of predicted outcomes in Wave 1, Wave 2, and their differences according to overall, treatment, and risk level based on marginal effects after multilevel regressions.Note: 1 Multilevel OLS Regression of N = 15181 rounds nested in N = 577 individuals (see Table S2, Models 4-5); 2 Logistic regression of N = 2588 groups/rounds (see Table S3, Models 2-3); 3 Multilevel OLS Regression of N = 15188 rounds nested in N = 577 individuals (see Table S4, Models 4-5); 4 Multilevel OLS Regression of N = 15183 rounds nested in N = 577 individuals (see Table S5, Models 4-5); 5 OLS regression of N = 2588 groups/ rounds (see Table S6, Models 2-3); Individual-level analyses of 1 , 3 , and 4 control for social value orientation, risk preferences, autism spectrum quotient, extraversion, agreeableness, conscientiousness, neuroticism, openness, age, gender, student, experience with experiments, and left-right political orientation.Analyses of 1 additionally control for empirical and normative expectations and personal normative belief; 6 Results based on exploratory analyses of three-way interactions between wave × treatment × disaster probability, see Model  Similarly to contributions, we find no average increase in the probability of reaching the threshold across the waves (All: ŷWave1 = 0.62 , ŷWave2 = 0.63 ; b All = 0.013, p = 0.470 , 95% CI [−.02, .05] ) so do not find support for Hypothesis 2. We also check whether there are differences across waves according to risk level and treatment, and, unlike for contributions, find that the between-wave difference on the group level does depend upon the treatment.Subjects in Low High are significantly and substantially likelier to reach the threshold in Wave 2 than in Wave 1 ( b LowHigh = 0.132 , p < 0.001 , 95% CI [0.082, 0.182]) and this result holds across both risk levels (Table 2).In High Low the opposite is true: subjects are less likely reach the threshold in Wave 2 ( b HighLow = − 0.98 , p < 0.001 , 95% CI [− 0.147, − 0.048] ).This difference is driven primarily by the decrease in the probability of reaching the threshold that happens following a decrease in risk.That is, in High Low 90 there is no difference between the waves (High Low 90: ŷWave1 = 0.82 , ŷWave2 = 0.78 ; b HighLow90 = − 0.037, p = 0.235 , 95% CI [− 0.10, 0.02] ), but there is a significant and substantial decrease in High Low 60 ( ŷWave1 = 0.47 , ŷWave2 = 0.31 ; b HighLow60 = − 0.160, p < 0.001 , 95% CI [− 0.23, − 0.09] ).This is shown by the round contrasts in Fig. 2B that have most red shapes above the 45 • diagonal line and most blue shapes below.
Result 2: Overall, groups were not likelier to reach the threshold in Wave 2 than in Wave 1.In Low High, reaching the threshold is higher in Wave 2, while in High Low reaching the threshold is lower in Wave 2.

Social norms: contents and strength
We do not find the expected average increase of empirical expectations ( ŷWave1 = 51.20 , ŷWave2 = 50.85; b All = − 0.352, p = 0.301 , 95% CI [−1.02, 0.31] ) so do not find support for Hypothesis 3. Turning to the between- wave differences according to risk level and treatment, we find that, like for contributions, empirical expectations under 90% risk were already greater than 50 in Wave 1 of both treatments (Low High 90%: ŷWave1 = 51.61, High Low 90%: ŷWave1 = 53.20 ) making it unsurprising that Wave 2 empirical expectations are not significantly higher (Low High 90%: ŷWave2 = 51.66 , High Low 90%: ŷWave2 = 52.81 ; comparisons to Wave 1 n.s.).Under 60% risk meanwhile, we find opposite differences according to treatment: an increase in empirical expectations in Low High ( ŷWave1 = 49.60 , ŷWave2 = 50.95; b LowHigh60 = 1.349, p = 0.004 , 95% CI [0.43, 2.27]; Fig. 3A) and a decrease Result 3: Average empirical expectations were not higher in Wave 2 than in Wave 1.In Low High 60%, empirical expectations are higher in Wave 2 and in High Low 60% they are lower in Wave 2.
Result 4: Normative expectations are not higher in Wave 2 than in Wave 1.In High Low 60% normative expectations are lower in Wave 2 than in Wave 1.
Result 5: Social norms are generally stronger in Wave 2 than in Wave 1.However, in High Low 60% social norms are weaker in Wave 2 than in Wave 1.

Behavioural types
We find the same behavioural profiles as in Wave 1 and in generally similar proportions (see Fig. 4A and B).Empirical cooperators (Wave 1: 11.6%, Wave 2: 9.0%) increase their contributions in response to higher empirical expectations, normative cooperators (Wave 1: 14.1%, Wave 2: 12.2%) increase their contributions when normative expectations are higher, social norm followers (Wave 1: 10.9%, Wave 2: 13.5%) increase their contributions in response to both higher empirical and higher normative expectations.We also find threshold-driven participants (Wave 1: 26.5%, Wave 2: 33.0%), in somewhat greater numbers than in Wave 1, who contribute around 50 points under all circumstances but slightly decrease contribution when others increase, and unconditional types (Wave 1: 37.0%, Wave 2: 32.2%), in somewhat smaller numbers than in Wave 1, who contribute around 50 points under all circumstances.
Consistent with Hypothesis 6a, we find that increasing normative expectations also increase the conditional contributions for all behavioural types irrespective of empirical expectations (see Fig. 4B and Supplementary Table S10).Some types increase their contributions a lot (e.g., Normative Cooperators increase their conditional contribution by 55 points for an increase in normative expectations if empirical expectations are low; b = 54.986, p < 0.001 , 95% CI [53.014, 56.96]), while others increase their contribution only slightly (e.g., a 4 point increase for Unconditional Types; b = 4.390 p < 0.001 , 95% CI [3.18, 5.60]).
Consistent with Hypothesis 6b, increasing empirical expectations does not increase contributions for all behavioural types.When normative expectations are low, most types respond to increasing empirical expectations by increasing their own contribution, but threshold-driven types instead reduce their contribution from 46.1 to 40. ).However, this does not classify them uncooperative or as free-riders, for their contributions remain around 50. Rather, normative cooperators and threshold-driven cooperators compensate for their group members when empirical expectations are low (contributing on average 63 points and 60 points, respectively).When empirical expectations increase, this compensation is no longer needed and they reduce their contributions to 51 points (normative cooperators) and 49 points (threshold-driven types) on average.
Result 6: We identify the same five behavioural types as in Wave 1 and these respond homogenously to an increase in normative expectations, but show heterogeneity in their behavioural response to an increase in empirical expectations.

Relationship between social norms and cooperation
Like in Wave 1, we find positive associations between empirical and normative expectations and contribution rates per round with one caveat: unlike in Wave 1, the positive association between normative expectations and contributions disappears after controlling for personal normative beliefs ( b = 0.077 , p = 0.265 , 95% CIs [− 0.06, 0.21] , see Supplementary Table S12).
We replicate the finding that contributions are causally and substantially influenced by empirical and normative expectations.When subjects are informed that the majority of group members contributes at least 50 points or believes one should contribute at least 50 points they significantly increase their contribution (see Supplementary Table S13 and Fig. S6).In Wave 1, the effect of normative expectations was stronger than that of empirical expectations.This effect is even more pronounced in Wave 2. The average contribution is 31 (95% CI [29.99, 32.51]) in response to low empirical and low normative expectations, it increases to 42 (95% CI [40.32,  42.84]) under high empirical and low normative expectations, and is further increases to 49 points when normative expectations are high-regardless of whether the high normative expectations are combined with low (95% CI [47.61, 50.13]) or high empirical expectations (95% CI [47.67, 50.20]).
Unexpectedly, we do not replicate the resilience of cooperative behaviour when moving from High to Low risk.In Wave 1 behaviour changed quickly after the change in risk in the Low High treatment, but norms exerted an inertia effect on behaviour in the High Low treatment.In Wave 2 we do not find this inertia effect for the High Low treatment.Instead, contributions in High Low drop immediately and significantly when risk changes, to levels even below the baseline of Low High (45.21 vs 50.04, b = − 4.833 , p < 0.001 , 95% CIs [− 7.23, − 2.44] ; see Supplementary Tables S16 and S17 and Figure S11).
Result 7: We replicate most of the findings concerning the relationship between social expectations and cooperation.Exceptions are that cooperative behaviour is not resilient when moving from High to Low risk, and that normative expectations do not correlate with contributions after controlling for personal normative beliefs.
To summarise, our hypotheses about Covid-19 generating differences in contributions, probability of reaching the threshold, and social norm content (expectations) are not supported.Our findings do support the hypothesis that Covid-19 increased social norm strength.Moreover, the data support the hypotheses about the homogeneous effect of a manipulation of normative expectations and a heterogeneous effect of the manipulation of empirical expectations.Importantly, behavioural types are replicated, which speaks of the relevance of our classification, and most of the relationship between behaviour and norms is also replicated, except the resilience of the norm moving from high to low risk.

Discussion
In this study we explored how cooperation and the associated social norms respond to collective disasters, with particular reference to disease threat like that posed by the Covid-19 pandemic.To this aim, we compared results of a collective-risk social dilemma experiment conducted before the pandemic (Wave 1, 2018) to the results from a replication of the same experiment that we collected near the height of the first Covid-19 pandemic wave (Wave 2, 2020).
On the basis of empirical evidence and theory, we predicted an increase of cooperative behaviours and social norms.Contrary to our expectations, we did not find this overall increase in cooperation and social norms in Wave 2. One reason for this result might be the very nature of our game, in which cooperation over an average of 50 is not efficient and therefore participants on average do not need to increase their efforts.Indeed, exploratory analyses reveal that the results depended on treatment and risk.In Wave 2, groups that start with a low disaster probability (60%) have stronger norms and are also significantly better at cooperating to reach the threshold compared to Wave 1.This advantage is revealed initially when groups face a low risk, but such improvement over Wave 1 continues to exist when risk increases to (90%).Such effect may indeed indicate that shared acquaintance with the pandemic might affect the alignment of social expectations and thereby increase the ability to coordinate with others: experience with the Covid-19 threat might have taught people to better estimate how others behave and how one should behave to avoid the disaster, even if the risk of that disaster is smaller.While in Wave 1 participants who started with a high disaster risk of 90% managed to cooperate and create strong social norms from the start more often than those starting in the low disaster risk; with the experience of the pandemic also participants that started with a lower, 60% risk mostly managed to cooperate.
Yet it remains unclear why social norms are weaker and why the ability to coordinate decreases in the low risk stage of the other, High Low treatment.Specifically, groups that start with a high disaster probability (90%) perform worse in Wave 2 compared to Wave 1 as cooperation decreases and social norms get eroded compared to Wave 1 when risk decreases to (60%) after 14 rounds.This pattern may suggest that during the Covid-19 pandemic, subjects might have realised that the need to cooperate-e.g., keeping social distance or wearing masks-is conditional on risk.When risk decreases, the possibility of getting infected becomes lower, and as such the need to cooperate.This might have translated into reduced (expectations about) cooperation in our experimental setting.This is a speculative explanation, though, that could not be tested with the available data.Further research based on data of (changes in) individual risk perception would be needed to better disentangle how norms and behaviour change in response to repeated recurrences of risk.
Even if some of our hypotheses were not confirmed, our findings have interesting theoretical implications.Contrary to our expectations grounded in the tightness-loose theory of cultures 17 , we do not have evidence that the global threat posed by the Covid-19 pandemic was sufficient to create a rapid general increase in cooperation and the underlying social norms.Evidence of the predicted increase is available only under specific scope conditions-suggesting, for instance, that the pandemic improved recognition of the potential disaster and the ability to cooperate when a risk is introduced, but that this is temporary and may break down as soon as the risk becomes less severe.Yet, this pattern of results may still be consistent with the broader theoretical stance.Indeed one possible explanation for our results could be that more time is needed for effects on norms and behaviour to emerge.Our study has been conducted in the first months of the pandemic and social behaviour and norms follow complex patterns that might differ between the short and long run.Another possibility is that different threats may strengthen different social norms, in particular those that are most relevant to overcome the specific threats faced.For example, pandemic threats might increase norms of hygiene, while hurricanes make stronger norms of helping.The cooperative task in the experimental study might have been perceived by subjects as not pertinent or too abstract to be relevant for the threat posed by the pandemic.This would be consistent with a cross-country study conducted at the beginning of the Covid-19 pandemic which found that in the short term, norms are largely stable to pandemic threats except for those norms that are perceived to be directly relevant to dealing with the collective threat, in particular hand washing norms 28 .Still, other research carried out comparing behaviours in countries under similar circumstances 19 showed a slightly significant increase in trust among infected people.While the authors conjectured that this could be due to receiving more cooperative behaviour when sick, we cannot make a clear connection with our results because we do not have separate data on infected versus non infected people.
Regardless, replicating the findings of our previous work 18 , this study provides evidence that under high risk (90% probability treatment), social norms become tighter and promote cooperation.Moreover, experience with the pandemic made participants more cooperative under 60% already in the Low High treatment.This is consistent with the core hypothesis of the tightness-looseness theory 17 .Recognising that social norms are strong drivers of cooperation is relevant to understanding how to design interventions to promote long-lasting cooperation in collective action problems characterised by risk.As the experience of the Covid-19 pandemic has made clear, in the mitigation of collective crises the use of messages that emphasise their risk and severity might not be effective as they can be paralyzing for people.If global challenges are perceived to be too big to be handled individually, this can evoke anxiety that might cause in people feelings of powerlessness and the impression that there's nothing we can do about it. 42,43Instead, interventions relying on social norms (or a combination of risk and norms) can appeal to a collective effort and to the fact that we can make it if we all act together.
On a fundamental level, our results also show how important social norms are to cooperation.Indeed, in the manipulations of expectations, both normative and empirical expectations substantially affect one's own contributions.This reinforces a key result from Szekely et al. 18 .Moreover, Wave 2 convincingly replicated the existence of behavioural types.Not only can participants be classified in the same groups, but even the percentage of each type in the population is approximately the same.This finding, along with related results in other experiments 44,45 , stresses the importance of recognizing different types of behavioural responses, for instance in the context of policy implementation.
Needless to say, our study presents several limitations.First, the cooperative behaviour in the task might be perceived as too abstract to be relevant for the specific risk posed by the Covid-19 pandemic.This might makes it difficult to study whether a change in a real collective risk, such as the one posed by the pandemic of Covid-19, is associated with changes in cooperative behaviour and social norms sustaining it.Second, we analyze short-time effects.Wave 2 has been conducted in the first months of the Covid-19 pandemic and the time frame might be too short to capture changes in social norms and behaviour.Third, our design cannot entirely identify the causal www.nature.com/scientificreports/effect of a variation in disease threat severity on the strength of social norms and cooperation.We cannot exclude that changes in norm strength and cooperation might have happened over time independent from the pandemic or other confounds nor did our design allow for a comparison between (pandemic-related) risk perceptions across waves.Fourth, in contrast with a one-shot design, the use of a paradigm with repeated but anonymous encounters allows the formation of group-level norms within the confine of an experimental setting.However for this very reason, this design choice may also reduce the identification of broader social norms that subjects bring to the lab from their everyday experience.Finally, we have employed a standard subject pool of university students.This should not be an issue for our between-waves comparison, since samples are similar between the waves, but it needs to be considered when generalizing our findings to the broader population.

Experiment
The replication experiment was conducted in the same way as the original experiment.On the first day, subjects completed the Big Five personality questionnaire, the Social Value Orientation slider measure, the Autism Spectrum questionnaire, and a risk preference elicitation task.On days 2-29, they participated in 28 rounds (one round per day) of the collective-risk social dilemma.At the end of the experiment (day 30), subjects' punishment behaviour and their expectations concerning punishment were elicited and they answered a short questionnaire on sociodemographics.The experiment was programmed in oTree.All interactions took place anonymously on computers or phones.On days 2-29, subjects were randomly allocated into groups of six each round.Every round, they received an endowment of 100 points and had to decide how much of their endowment to contribute to a collective fund.If a threshold amount (300 points) was reached, subjects kept as that round's earnings the share of their endowment not contributed to the collective fund.If the threshold was not reached, with some probability p they lost their entire endowment, while with probability 1 − p they kept what they did not contribute to the collective fund.Subjects that participated in the treatment High Low faced a 90% risk in rounds 1-14 and a 60% risk in rounds 15-28.Subjects in the treatment Low High first faced the 60% risk and after 14 days switched to the 90% risk.
Contribution decisions were made simultaneously and anonymously.To study whether social norms were formed, each round we elicited subjects' Personal Normative Beliefs (PNB), Empirical Expectations (EE), and Normative Expectations (NE) randomly either before or after they made their contribution decision.The EE decisions were incentivised by comparing them against the group members' contributions; the NE decisions were incentivised by comparing them against the group members' PNBs.At the end of each round subjects were informed about the contribution decisions of the group members.In rounds 1, 5, 10, 14, 15, 19, 24, 28, subjects were presented with additional conditional contribution questions in which they were asked for their hypothetical contributions in case the majority of their group members would contribute [at least 50 points/ less than 50 points] and believed one should contribute [at least 50 points/less than 50 points].These questions were incentivised by paying the subjects based on their answer to the EE and NE combination that was realised in the subject's group.

Figure 1 .
Figure 1.Experimental design.Note: Each day represents an experimental round.On day 1, participants performed four individual trait tests: Big Five, risk preference elicitation, Autism spectrum and Social ValueOrientation, and completed a short questionnaire.From day 2 to day 29 participants were matched in groups of six people and interacted according to the collective risk social dilemma answering questions on their expectations (asked in a random order with 50/50 probability either before or after the contribution decision) and deciding their actual contribution and their conditional contributions.Conditional contributions were elicited on rounds 1, 5, 10, 14, 15, 19, 24, and 28.At the end of each round, participants kept their saved points if the threshold was reached, otherwise they lost all their round points with probability p.The outcome of the conditional contribution decisions was calculated based on the contributions and actual empirical and normative expectations of each group (see Supplementary Information Section S1 for details).Each day the groups were reshuffled.On day 30, participants went through a punishment phase in which their punishment behaviour and expectations were elicited.Subjects subsequently received information about their results and payment.Figure reproduced from18 .

Figure 2 .
Figure 2. Scatter plots for contribution (individual level) and threshold reached (group level) in Wave 1 and Wave 2. Note: Green circle: All data; Blue square: Low High Treatment, 60% Risk; Blue diamond: Low High Treatment, 90% Risk; Red diamond: High Low Treatment, 90% Risk; Red square: High Low Treatment, 60% Risk.The area above the dashed diagonal indicates an increase in Wave 2 compared to Wave 1; the area below indicates a decrease.Dark solid shapes with confidence intervals represent the average predictor per category (All, LH60, LH90, HL90, HL60).Transparent shapes represent the average predictors per round.

Figure 3 .
Figure 3. Scatter plots for empirical expectations, normative expectations (individual level), and norm strength (group level) in Wave 1 and Wave 2. Note: Green circle: All data; Blue square: Low High Treatment, 60% Risk; Blue diamond: Low High Treatment, 90% Risk; Red diamond: High Low Treatment, 90% Risk; Red square: High Low Treatment, 60% Risk.The area above the dashed diagonal indicates an increase in Wave 2 compared to Wave 1; the area below indicates a decrease.Dark solid shapes with confidence intervals represent the average predictor per category (All, LH60, LH90, HL90, HL60).Transparent shapes represent the average predictors per round.

Figure 4 .
Figure 4. Behavioural type clusters and their conditional contributions in Wave 2. Note: EC, empirical cooperator; SNC, social norm cooperator; NC, normative cooperator; U, unconditional; TD, threshold-driven.Empirical (Normative) Expectations Influence is calculated by taking the difference in conditional contributions for High and Low EE (NE) averaged for when NE (EE) are high and low.Low EE (NE) refers to the hypothetical situation that the majority of the group contributes (thinks one should contribute) less than 50 points.High EE (NE) refers to the hypothetical situation that the majority of the group contributes (thinks one should contribute) at least 50 points.